电容取值对RLC串并联谐振电路实验误差的影响

1、论文分类号：O441.1密 级：论 文 题 目 电容取值对RLC串/并联谐振电路实验误差的影响 目 录摘 要1引 言21 实验部分31.1 实验设备31.2 电容取值对RLC串联谐振电路实验误差的影响31.3 电容取值对RLC并联谐振电路实验误差的影响52 结果与讨论62.1电容取值对RLC串联谐振电路实验数据的分析62.2 电容取值对RLC并联谐振电路实验数据的分析73 结 论8参考文献9电容取值对RLC串/并联谐振电路实验误差的影响摘 要：RLC串/并联谐振是交流电路中的一种特殊现象，在电工技术和无线电中得到广泛的应用。本论文通过确定电阻和电感值，采用测量电路中电阻或电容两端电压为最大值的

2、办法来确定谐振频率，讨论了电容数值对测量误差的影响。实验结果表明，不论在串联谐振还是并联谐振实验中，都是电容取值越小，谐振频率的测量值越准确。关键词：RLC串/并联电路；电容；谐振频率The effect of the capacitance on the RLC series/parallel resonanceZhang Jing(Class 5 Grade 2010 in College of Physics, Jilin Normal University, Jilin Siping 136000)Directive teacher: Wang Li (lecturer)Abstrac

3、t: RLC series / parallel circuit is a particular phenomenon in ac circuit, and widely be used in fields of electrical technology and radio. In this paper, we study the effect of the capacitance on the RLC series/parallel resonance through measuring the maximum of voltage of the resistor or capacitor

4、. The results show that the value of capacitance is smaller; the accuracy of RLC series / parallel circuit is the better.Key words: RLC series / parallel circuit; the capacitance; resonant frequency引 言RLC串/并联谐振是交流电路中的一种特殊现象，在电工技术和无线电中得到广泛的应用。对于RLC串/并联谐振，普通物理实验通常要求在品质因数Q1的情况下，采用测量电路中电阻或电容两端电压为最大值的办法来

5、确定谐振频率。串联RLC电路由电阻、电感和电容组成的。由于感抗和容抗对电路相位角的作用相反，所以总的电抗小于任何一个单独的电抗。已知容性阻抗随频率增大而减小，感抗随频率增大而增大。图1是RLC串联电路中总电抗的变化规律：电源频率逐渐增大，当频率非常小时，容抗较高，感抗较低，电路呈电容性。随着频率的逐渐升高，容抗随之减小，感抗逐渐增大，当容抗等于感抗的时候，两者的电抗效应互相抵消，电路可以简化为纯电阻电路，即串联谐振的条件。随着频率的继续增大，感抗大于容抗，这时电路为电感性的。图1 RLC串联电路XC和XL随频率变换的曲线当XC=XL时，RLC串联电路发生谐振，发生谐振的频率叫做串联谐振频率，串

6、联谐振又称作电压谐振。并联RLC电路也是由电阻、电感和电容组成的。在并联电路中，感抗越小对电路的影响就越大，因为电抗越小，支路电流就越大。当频率较低时，XCXL,电路呈感性的。随着频率的增大，容抗减小，感抗增大，当XC=XL时，就是并联谐振，又称为电流谐振，此时的频率为RLC并联谐振频率。当频率继续增大时，XCXL,电路呈容性的。本文采用测量电路中电阻或电容两端电压为最大值的办法来确定RLC串/并联谐振频率的实验值，电容取值对谐振频率测量的影响。1 实验部分1.1 实验设备 表1 实验所用设备名称型号出厂商信号发生器YB163P电阻箱ZX38A/10交/直流自感器BG 6/4型标准十进制电容箱

7、RX7型交流毫伏表AS2173D1.2 电容取值对RLC串联谐振电路实验误差的影响图2 RLC串联电路图电路图见图2，已知电感内阻RL=20,电阻取值50、100和150。电容C取值分别为0.01F、0.03F、0.05F、0.1F、0.15F、0.2F、0.3F、0.4F和0.5F。测量时保持a、b两端电压为1.06V。用交流毫伏表测电阻两端电压，当电压为最大时，电路达到谐振状态。记录此时的频率值，即谐振频率的测量值f测，连续测量五次，求其平均值f平均，实验数据见表2。表2 串联电路R与C取不同值时测量的谐振频率的测量值 f测量C/Ff测量1（kHz）f测量2（kHz）f测量3（kHz）f测

8、量4（kHz）f测量5（kHz）f 平均（kHz）R=500.010.020.030.050.10.150.20.30.40.54.9953.5722.8922.2421.5871.3091.1320.9170.7880.7094.9853.5482.8842.2531.5911.2901.1170.9140.7900.7154.9903.5592.9012.2431.6031.3021.1210.9240.8020.7135.0213.5682.8982.2331.5921.3041.1260.9200.7950.7064.4843.5512.9052.2411.5901.2981.1240

9、.9110.7850.7074.8953.55922.8962.24181.59261.30061.1240.91720.7920.71R=1000.010.020.030.050.10.150.20.30.40.55.0103.5582.8832.2711.5501.3211.1410.9520.7610.6984.9993.5502.8922.2681.5591.3341.0800.9660.7690.6995.0063.5552.9012.2391.5671.3401.1580.9550.7780.7465.0093.5562.9092.2471.5711.3371.1290.9690.

10、7710.7505.0013.5572.9122.2571.5731.3411.1130.9630.7640.7055.00463.55722.89942.25641.5641.33461.12420.9610.76860.7196R=1500.010.020.030.050.10.150.20.30.40.55.0043.5752.8992.2481.6021.3091.1230.9170.7890.7115.0283.5552.9112.2401.5941.2961.1190.9250.7900.7125.0133.5602.9122.2531.5971.3021.1270.9340.79

11、40.7045.0083.5652.9122.2541.5901.2921.1230.9200.8010.7094.9973.5672.9022.2561.5861.2951.1240.9120.7960.7095.013.56442.90422.25021.59381.29881.12320.92160.7940.70861.3 电容取值对RLC并联谐振电路实验误差的影响表3 并联电路R与C取不同值时测量的谐振频率的测量值 f测量C/Ff测量1（kHz）f测量2（kHz）f测量3（kHz）f测量4（kHz）f测量5（kHz）f 平均（kHz）R=00.010.020.030.050.10.1

12、50.20.30.40.55.0013.6383.1822.2741.6361.3211.0540.8600.5820.4685.0773.6913.2322.3081.6571.3401.0700.8190.5930.3015.0613.4322.9162.2021.5611.2511.1610.9020.6360.3075.0173.6782.9632.2351.5811.2691.1770.9100.6520.4574.9843.7343.1122.2541.6081.2961.1150.8990.6120.4725.0283.63463.0812.25461.60861.29541.1

13、1540.8780.6150.41R=300.010.020.030.050.10.150.20.30.40.54.8263.6192.9682.4891.6261.1511.1150.8910.8050.3254.9623.5512.9732.5751.6461.1571.1250.8940.8160.3304.9253.5922.9822.5441.6201.1411.1200.9030.8810.2374.8373.5672.9922.4891.6351.1501.1230.8960.8120.2334.8793.5923.0142.4921.6481.1451.1170.8900.80

14、90.3244.8863.58422.98582.51791.6351.14881.120.89480.81060.2898R=500.010.020.030.050.10.150.20.30.40.55.0003.6833.0062.3011.4581.2561.1410.9150.5810.6994.9193.7413.0222.2691.4501.2371.1590.9040.5890.6954.9253.6012.9162.2981.4741.2411.1280.9070.5870.6934.9903.5922.9232.3051.4821.2651.1470.9100.5860.70

15、04.7213.6273.0102.2571.4631.2531.1490.9120.5820.7024.9113.64922.98742.2851.46541.25041.14480.90960.5850.6978图3 RLC并联电路图 电路图见图3，已知电感内阻RL=20,电阻取值0、20和50。电容C取值分别为0.01F、0.03F、0.05F、0.1F、0.15F、0.2F、0.3F、0.4F和0.5F。测量时保持R1两端电压为1.5V。当电路中电容两端电压为最大时，电路达到谐振状态。记录此时的频率值，即谐振频率的测量值f测量，连续测量五次，求其平均值f平均，实验数据见表3。2 结果与

16、讨论2.1电容取值对RLC串联谐振电路实验数据的分析表4 RLC串联电路R与C取不同值时测量的谐振频率的理论值及C/F/kHzR=50R=100R=1500.015.00460.97810.99401.00110.023.55721.00060.99901.00200.032.89940.99880.99731.00170.052.25640.99351.00240.99730.11.56401.01830.98201.01910.151.33460.97451.02600.97320.21.12420.99980.99800.99910.30.96100.95441.00500.95900.

17、40.76861.03040.96551.03300.50.71960.98671.01100.9855已知谐振频率的理论值为 （1）根据上式可以求出电容取不同值时各电路的谐振频率理论值以及（=f平均/f理论）的数值，如表4。图4给出了串联谐振中与电容C的曲线关系。由图可以看出当电阻电感取值一定时，电容C取值越小，的数值越接近于1。所以在RLC串联电路中当电阻R和电感L取值一定时，C取值越小，谐振频率的实验值越接近于理论值，即实验误差越小。图4 串联谐振中与电容C的曲线关系2.2 电容取值对RLC并联谐振电路实验数据的分析已知谐振频率的理论值为 （2） 其中R=R+RL，根据上式可以求出不同电

18、路的谐振频率理论值f理论以及的数值，如表5。图5给出了并联谐振中与电容C的曲线关系。由图可以看出当电阻R电感L取值一定时，电容C取值越小，的数值越接近于1。所以在RLC并联电路中当电阻R和电感L取值一定时，C取值越小，谐振频率的实验值越接近于理论值，即实验误差越小。表5 RLC并联电路R与C取不同值时测量的谐振频率的理论值及C/F/kHzR=0R=30R=50R=0R=30R=500.015.03545.03235.03170.99850.97090.97600.023.56053.55793.55711.02081.00741.02590.032.90712.90472.90361.0598

19、1.02791.02890.052.25172.49382.24801.00131.00961.01640.11.59201.58961.58771.01041.02860.92300.151.29981.29711.29470.99660.88570.96550.21.12551.12261.11990.99100.99771.02230.30.91870.91540.91210.95570.97750.99720.40.79550.79180.78790.77311.02380.74240.50.71140.70730.70300.56370.40970.9926图5 并联谐振中与电容C的曲线关系3 结 论 本论文研究了电容对RLC串/并联谐振电路谐振频率测量的影响。在固定电阻和电感数值的情况下，多次改变电容值，并根据通过测量电阻/电容两端最大